by Dr. Bruce McLaughlin
This article presents evidence suggesting that the nine elements of the CKM Matrix, which are integral to the Standard Model of Particle Physics, flow from the first twelve characters of the first verse of Genesis.
Introduction
A Judeo-Christian tradition is that God arranged the 304,805 character string of concatenated words in the Torah to reveal not only a spiritual message but also to encrypt fundamental information about the beginning of the universe and its development over time including the entirety of physics, chemistry, biology and human history… a message within a message.
In Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin, several critical dimensionless numbers of physics/mathematics are predicted from the first 12 characters of the first verse of Genesis. Is it possible that this same string of 12 characters provides information about fundamental parameters of particle physics?
Background
The magnitudes of the nine CKM matrix elements are given by:
0.97427 (+0.00015 0.22534 (+0.00065 0.00351 (+0.00015
-0.00015) -0.00065) -0.00014)
0.22520 (+0.00065 0.97344 (+0.00016 0.0412 (+0.0011
-0.00065) -0.00016) -0.0005)
0.00867 (+0.00029 0.0404 (+0.0011 0.999146 (+0.000021
-0.00031) -0.0005) -0.000046)
These magnitudes indicate the probability of transition from one quark to another.
Analysis
The first three, second three and third three characters from the first verse of Genesis can be expressed as
| |
|
020 |
|
|
|
212 |
|
|
|
020 |
| Ayz |
= |
000 |
|
Byz |
= |
001 |
|
Cyz |
= |
000 |
| |
|
110 |
|
|
|
200 |
|
|
|
110 |
reading left to right as the Text is read from right to left. Each of the Hebrew characters is represented by a base-3 triplet (column vector) according to a rule that starts with Aleph as (000) and ends with Tsadey Final as (222). If these three matrices are arranged in a Rubik Cube configuration, fifteen 3 by 3 matrices are produced by taking slices through the cube. Each slice produces 8 matrices by rotation about various axes; dihedral group of order eight (D4). In this trial, only one matrix will be selected for each slice. We still find ourselves short by one 3 by 3 matrix in order to construct a single matrix of dimension 12. We will add a single 3 by 3 matrix representing the fourth three characters from the first verse of Genesis.
A 12 by 12 matrix M can be constructed from these four matrices as illustrated in Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin. This matrix M is:
| 0 |
2 |
0 |
2 |
1 |
2 |
0 |
2 |
0 |
1 |
2 |
1 |
| 0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
2 |
0 |
0 |
1 |
1 |
0 |
0 |
2 |
0 |
| 0 |
2 |
0 |
2 |
1 |
2 |
0 |
2 |
0 |
0 |
2 |
0 |
| 0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
| 0 |
0 |
0 |
1 |
0 |
1 |
1 |
2 |
1 |
1 |
1 |
0 |
| 0 |
2 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
| 2 |
1 |
2 |
0 |
0 |
1 |
2 |
0 |
0 |
0 |
0 |
1 |
| 0 |
2 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
0 |
2 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
| 0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
| 0 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
1 |
Now define X = MM*, Y = X2 and Z = X3 where M* is the transpose of M. X, Y and Z are each 12 by 12 matrices and each will have a characteristic equation with twelve coefficients. Let the coefficients for X, Y and Z be denoted by J1…J12, JJ1…JJ12 and JJJ1…JJJ12 respectively. Next form the following 6 by 6 matrix, designated as j1, from the 36 coefficients of the three characteristic equations?
JJJ1 J1 J2 JJJ12 JJJ11 J12
JJJ2 J6 J3 JJ7 JJ8 JJ9
j1 = JJJ3 JJ1 J7 JJ6 J10 JJ10
JJJ4 JJ2 J4 J8 J5 JJ11
JJJ5 JJ3 JJ4 JJ5 J9 JJ12
JJJ6 JJJ7 JJJ8 JJJ9 JJJ10 J11
This particular matrix is just one of 36! matrices that can be formed from the 36 coefficients. Now form the symmetric matrix k1 = j1 j1* and evaluate cosk1 = Cos[k1], sink1 = Sin[k1], p1 = Cos2[k1], q1 = Sin2[k1] and r1 = Sin[k1]Cos[k1]. These five expressions use the power series for Sin and Cos with ordinary powers replaced by matrix powers. The result is five, 6 by 6 symmetric matrices with the absolute value of each element between zero and one. So, how might CKM magnitudes be encoded? One way is to combine no more than two selected matrix elements from p1, q1 and r1 using basic arithmetic – addition, subtraction, multiplication and division – while viewing the elements themselves as floating point numbers; in other words, the decimal point can be shifted to the right or left. Here is a sample finding:
CKM11 = 10 r1[[2,3]] + 10-1 r1[[2,2]] = 0.974345
CKM22 = 10 r1[[2,3]] – 10 p1[[1,3]] = 0.973407
CKM33 = 10 r1[[2,3]] -10 r1[[1,4]] = 0.999177
CKM12 = - r1 [[2,2]] + 10 q1[[4,5]] = 0.225462
CKM21 = - r1[[2,2]] + 10-1 r1[[2,2]] = 0.225031
CKM13 = r1[[3,4]] = 0.0035343
CKM31 = 103 r1[[3,5]] + 10 r1[[1,4]] = 0.0086507
CKM23 = - 10-1 r1[[5,5]] + 10-2 r1[[2,2]] = 0.0413213
CKM32 = - 10-1 r1[[5,5]] – r1[[3,4]] = 0.0402874
Conclusions
The predicted CKM matrix from this sample is:
0.974345 0.225462 0.0035343
0.225031 0.973407 0.0413213
0.0086507 0.0402874 0.999177
which is consistent with the confidence limits of the actual CKM Matrix of Magnitudes. Also, only seven elements of r1, one element of p1 and one element of q1 were used to define these nine elements. This suggests a functional relationship exists between the various elements of the CKM matrix.
These findings could represent a completely serendipitous coincidence. Or they might suggest a causal connection between God and the Standard Model of Particle Physics. At the very least, these findings demonstrate how the CKM Matrix of Magnitudes can be generated from four 3 by 3 matrices with elements 0, 1 and 2 where two of the matrices are identical.
